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Unformatted text preview: lecture 4, Probability I The Concept of Probability Sample Spaces and Events Some Elementary Probability Rules lecture 4, Probability I Outline • The Concept of Probability • Sample Spaces and Events • Some Elementary Probability Rules • Conditional Probability and Independence lecture 4, Probability I The Concept of Probability Sample Spaces and Events Some Elementary Probability Rules lecture 4, Probability I The Concept of Probability • An experiment is any process of observation with an uncertain outcome • The possible outcomes for an experiment are called the experimental outcomes • Probability is a measure of the chance that an experimental outcome will occur when an experiment is carried out lecture 4, Probability I The Concept of Probability Sample Spaces and Events Some Elementary Probability Rules lecture 4, Probability I The Concept of Probability Probability • If E is an experimental outcome, then P ( E ) denotes the probability that E will occur and: • Conditions • ≤ P ( E ) ≤ 1 such that: • If E can never occur, then P ( E ) = • If E is certain to occur, then P ( E ) = 1 • The probabilities of all the experimental outcomes must sum to 1 lecture 4, Probability I The Concept of Probability Sample Spaces and Events Some Elementary Probability Rules lecture 4, Probability I The Concept of Probability Assigning Probabilities to Experimental Outcomes • Classical Method • For equally likely outcomes • Long-run relative frequency • long run • Subjective • Assessment based on experience, expertise or intuition lecture 4, Probability I The Concept of Probability Sample Spaces and Events Some Elementary Probability Rules lecture 4, Probability I The Concept of Probability Classical Method • All the experimental outcomes are equally likely to occur • Example: tossing a “fair” coin • Two outcomes: head (H) and tail (T) • If the coin is fair, then H and T are equally likely to occur any time the coin is tossed • So P ( H ) = . 5, P ( T ) = . 5 • &lt; P ( H ) &lt; 1,0 &lt; P ( T ) &lt; 1 • P ( H ) + P ( T ) = 1 lecture 4, Probability I The Concept of Probability Sample Spaces and Events Some Elementary Probability Rules lecture 4, Probability I The Concept of Probability Long-Run Relative Frequency Method • Sometimes it is either difficult or impossible to use the classical method to assign probabilities, we can estimate the probability of the experimental outcome to be the proportion of the time that the outcome occurs during the many repetitions of the experiment....
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